To tell if two lines are , we check if their are negative . For this exercise, we have been given two points on each line, so we have enough information to calculate their slopes using the .
m=x2−x1y2−y1
Note that when choosing points to substitute for
(x1,y1) and
(x2,y2), it doesn't matter which points on the line you choose, since the result will be the same. Let's start with line
ℓ1, which passes through
(-3,4) and
(1,-2).
m=x2−x1y2−y1
m=1−(-3)-2−4
m=-23
The slope of line
ℓ1 is
-23. We will use the same method to identify the slope of line
ℓ2.
Line
|
Points
|
x2−x1y2−y1
|
Slope
|
Simplified Slope
|
ℓ1
|
(-3,4)&(1,-2)
|
1−(-3)-2−4
|
4-6
|
-23
|
ℓ2
|
(-4,0)&(2,4)
|
2−(-4)4−0
|
64
|
32
|
To determine whether or not the lines are perpendicular, we calculate the product of their slopes. Any two slopes whose product equals -1 are negative reciprocals, and therefore the lines are perpendicular.
-23(32)=-1
We have found that lines ℓ1 and ℓ2 are perpendicular to one another.